Exact solutions of the QCD evolution equations using Monte Carlo method

TL;DR

This paper develops a Monte Carlo method to solve QCD evolution equations for parton distributions with high precision, highlighting advantages over traditional methods and proposing future non-Markovian algorithm development.

Contribution

It introduces an exact Monte Carlo approach for solving QCD evolution equations, demonstrating its precision and advantages over existing non-MC methods.

Findings

Achieved ~0.1% accuracy in numerical solutions

Highlighted advantages of Markovian Monte Carlo over non-MC methods

Outlined challenges for developing non-Markovian Monte Carlo algorithms

Abstract

We present the exact and precise (~0.1%) numerical solution of the QCD evolution equations for the parton distributions in a wide range of $Q$ and $x$ using Monte Carlo (MC) method, which relies on the so-called Markovian algorithm. We point out certain advantages of such a method with respect to the existing non-MC methods. We also formulate a challenge of constructing non-Markovian MC algorithm for the evolution equations for the initial state QCD radiation with tagging the type and $x$ of the exiting parton. This seems to be within the reach of the presently available computer CPUs and the sophistication of the MC techniques.